The Potter family begins with John Potter born early 1800s.  John had a son named: 

James Potter, born 1846, Co. Leitrim. James was a policeman dated 16.10.1883, Newport and a Sergeant (R.I.C) 23.05.1892, Croghan, Co. Roscommon.  James moved to Leckneen, Turlough, Co. Mayo and died in March 1927.  James married Agnes Beckett (1863 - 1952) from Turlough, Co Mayo on the 16.10.1883, COI, Castlebar, Mayo. 

Mayo Examiner 20 October 1883. POTTER - BECKETT - on the 16th of October, at Turlough, Presbyterian Church, by the Rev. James Steen, James Potter, Sergeant, R.I.C., Newport, to Agnes, daughter of Mr James Beckett, Ballyguin, Turlough. 

Agnes Beckett was the daughter of James Beckett (B. C.1824 - D.1909), and Elizabeth McAdam (B. C.1828 - 1896 - daughter of James McAdam, Presbyterian Church), and granddaughter of Isaac Beckett and Mary Lindrum. Agnes was one of fifteen children. James Potter died in 1927, aged 81 years.

Children of James and Agnes:

i William Potter B. 1884

ii Jane Potter B. 09.10.1885. Married John Eyre Heaphy on the 18.01.1909, COI, Doonfeeny, Killala, Co. Mayo. John Eyre Heaphy, was the son of John Eyre Heaphy and Mary Jane Boyd, and grandson of Eyre Heaphy and Harriet Vokes, Limerick.  He was a constable (R.I.C.), SS Police, Belfast and Lance Corporal (Lord Strathcona's Horse). Died 07 April 1918, Mauberg-Centre Cemetery, France). [See Heaphy Family Page]. Children of John Eyre and Jane: 

Olive Kathleen Heaphy B. 04.08.1913. No further information is available on Olive Heaphy. 

Jane Potter Heaphy marries again on the 26 September 1921 to Edmund Alexander Bolster of Belfast and has two sons, Edmund (1923) and Richard (1927).  Jane dies 22 January 1961, Belfast.  

iii Isaac Potter B. 1887 died 1887, Castlebar district, Mayo. 

iv Elizabeth Potter B. 1888

v Emily Potter B. 1890

vi James Arthur Potter B. 1892

vii Robert John Potter B. 1895

viii David Beckett Potter B. 1899. 

Note: 

It is unclear if the Potter family originated from England. James Potter, father of Jane Potter, was born in Co. Leitrim, with only records of small number of families for the county, all COI, with two earlier origins for a John Potter, born early 1800s:

John Potter (1799 - 1880) of Kilcoosy, Leitrim, whose wife was Susan (1811 - 1891) with a son Jackson Potter (1839 - 1926), Kilcoosy, who married Anne Jane Roycroft, COI, in 1868. Jackson and Anne Jane had the following children: Robert Potter, Mary Anne Potter and Susan Potter. 

John Potter (1808 - 1895) of Kilcoosy, Leitrim, whose wife was Anne (1815 - 1887). John's daughter was Eliza Potter (1854 - 1882) and a son Edward Potter (1854 - 1904), who married Rebecca Robinson (dau. of Rutledge Robinson), COI, in 1880. Edward and Rebecca had the following children: Thomas Potter, Elizabeth Jane Potter, Anne Potter, Sarah Potter, John Potter, Edward Potter, Rutledge Potter, and Rebecca Potter. 

William Potter (1808 - 1876), of Kilcoosy, Leitrim. A John Potter present as his death. 

There is also a record for Irwin Potter (B. C.1840), of Kilcoosy, Leitrim, a son of one of the above John Potter or William Potter. Irwin married Mary Maley, COI, in 1865, and the couple immigrated to New York, U.S. The 1870 census for New York shows Irwin and Mary with the following children: Emily Potter, Jessie Potter, and Willie Potter. 

1911 Census shows a John Potter (B. C.1834) and his sister Margaret Potter, of Kilcoosy, Leitrim.